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. 2017 Aug 24;12(8):e0183621.
doi: 10.1371/journal.pone.0183621. eCollection 2017.

Exploring virus release as a bottleneck for the spread of influenza A virus infection in vitro and the implications for antiviral therapy with neuraminidase inhibitors

Laura E Liao  1 , Szymon Kowal  1 , Daniel A Cardenas  1 , Catherine A A Beauchemin  1   2
Affiliations

Exploring virus release as a bottleneck for the spread of influenza A virus infection in vitro and the implications for antiviral therapy with neuraminidase inhibitors

Laura E Liao et al. PLoS One. .

Abstract

Mathematical models (MMs) have been used to study the kinetics of influenza A virus infections under antiviral therapy, and to characterize the efficacy of antivirals such as neuraminidase inhibitors (NAIs). NAIs prevent viral neuraminidase from cleaving sialic acid receptors that bind virus progeny to the surface of infected cells, thereby inhibiting their release, suppressing infection spread. When used to study treatment with NAIs, MMs represent viral release implicitly as part of viral replication. Consequently, NAIs in such MMs do not act specifically and exclusively on virus release. We compared a MM with an explicit representation of viral release (i.e., distinct from virus production) to a simple MM without explicit release, and investigated whether parameter estimation and the estimation of NAI efficacy were affected by the use of a simple MM. Since the release rate of influenza A virus is not well-known, a broad range of release rates were considered. If the virus release rate is greater than ∼0.1 h-1, the simple MM provides accurate estimates of infection parameters, but underestimates NAI efficacy, which could lead to underdosing and the emergence of NAI resistance. In contrast, when release is slower than ∼0.1 h-1, the simple MM accurately estimates NAI efficacy, but it can significantly overestimate the infectious lifespan (i.e., the time a cell remains infectious and producing free virus), and it will significantly underestimate the total virus yield and thus the likelihood of resistance emergence. We discuss the properties of, and a possible lower bound for, the influenza A virus release rate.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Modelling influenza A virus infection with and without explicit release.
In an influenza A virus infection, the virion gains entry into the cell when hemagglutinin (HA) proteins on the surface of virions bind to sialic acid receptors on the surface of the target cell. As viral replication gets underway, increasing amounts of viral proteins such as HA and neuraminidase (NA) are expressed on the cell surface. Throughout the infection, the density of sialic acid receptors declines as NA cleaves them. After viral replication takes place in the nucleus, the viral RNA progeny is transported to the cell membrane for virus assembly and budding. Some progeny virions will be released as free virus (V), while others remain bound (Vb) to the cell surface upon exiting the cell when HA on the surface of budded virion binds to sialic acid on the cell. The simple MM without an explicit term for viral release encapsulates these later processes implicitly as a part of the parameter quantifying free virus production (p) by infectious cells (I). The release MM has an explicit term for viral release at a rate r, which occurs after bound virus is produced at a rate p onto the surface of the cell. In both MMs, all virions, bound (Vb) or free (V), lose infectivity at rate c.
Fig 2
Fig 2. The role of explicit viral release on free and bound virus kinetics.
(A) The concentration of free virus titer from an in vitro infection experiment with the 2009 pandemic influenza A (H1N1) virus strain [20] was simulated in the simple MM (red), which serves as our baseline simulation. The baseline is compared to the free virus titer simulated in the release MM (black) where the release rate, r, is varied from 10−4 h−1 to 10−2 h−1, and all other parameters are kept at their base values. Note that when r ≥ 100 h−1, the release MM reduces to the simple MM. For low release rates, the free virus is suppressed compared to the baseline (black vs red), but is unaffected when r is greater than a critical value of rf = 3 h−1−5 h−1 (teal). (B) The corresponding concentration of bound virus in the release MM is shown (black), where the bound virus titer peak is maximal at another critical value of the release rate, rb = 3 × 10−3 h−1 (purple).
Fig 3
Fig 3. Simultaneous fits of the release MM to the simulated free virus titer of the SC, MC, MY assays.
The release MM was simultaneously fitted to the free virus titer from the (A) SC, (B) MC, and (C) MY assays simulated using the simple MM (red; using base parameters). The production rate, infection rate, rate of loss of virion infectivity, eclipse length, and infectious lifespan were fitted. Fitted curves are shown for a high (r = 1 h−1, black), an intermediate (r = 0.1 h−1, green), and a low (r = 0.01 h−1, blue) release rate.
Fig 4
Fig 4. Comparing parameter estimates between the simple MM and release MM.
The simple MM base parameters of an in vitro infection with the 2009 pandemic influenza A (H1N1) virus strain [20] are shown (red) with 95% confidence intervals (grey band). For the release MM, the parameter estimates obtained (y-axis) as a function of the viral release rate (x-axis) are shown for the case when all parameters (p, β, c, τE, τI) are estimated (black), or for the case with the constraint prelease = psimple(r + c)/r (blue). The critical free virus release rate, rf = 3.7 h−1, is indicated (vertical dotted line).
Fig 5
Fig 5. Simultaneous fits of the release MM to the simulated SC, MC, MY titers with a constraint on virus production.
As in Fig 3, but with a constraint on the virus production rate, i.e., prelease = psimple(r + c)/r where psimple = 6.28 × 108(PFU/mL) ⋅ h−1.
Fig 6
Fig 6. Comparing the effect of NAIs in the simple and release MMs.
(A) For slow virus release (r = 0.01 h−1), both MMs predict a similar viral kinetic time course for treatment with NAI at a constant efficacy of 0.99, compared to the untreated infection (blue dotted line). (B) With faster virus release (r = 10 h−1), the simple MM predicts more significant viral yield suppression than the release MM for the same NAI efficacy. (C) The (1 − εcrit) of NAIs in the simple MM (red solid line) and the release MM (blue dashed line) is shown as a function of the release rate. The vertical dotted lines in (C) indicate the release rates used in (A) and (B).
Fig 7
Fig 7. Comparing antivirals that inhibit release to antivirals that inhibit production in the release MM.
(A) The (1 − εcrit) of an antiviral that inhibits virus production (εp, solid) is compared to that of an antiviral that inhibits release (εr, dashed). The vertical dotted lines indicate the release rates in (B) and (C). (B) With slow release (r = 0.01 h−1), the release MM predicts a similar viral kinetic time course for treatment with either antiviral at an efficacy of 0.999. The untreated infection is shown (dotted). (C) With rapid release (r = 10 h−1), the release MM predicts that an antiviral that inhibits virus production suppresses viral yield significantly more one inhibiting virus release, for the same efficacy.
Fig 8
Fig 8. Instabilities in numerically solving model ordinary differential equations (ODE).
Numerically solving ODEs in Eqs (1)–(7) (blue) results in instabilities, however solving transformed Eqs (13)–(19) (red) resolves the issue.
Fig 9
Fig 9. Comparing the AICC of release MM fits.
The corrected Akaike information criterion (AICC) is shown for fits to the release MM with a constraint on the virus production rate (Npar = 4, blue), and without a constraint (Npar = 5, black).
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Grants and funding

This work was supported in part by Discovery Grant 355837-2013 from the Natural Sciences and Engineering Research Council of Canada (www.nserc-crsng.gc.ca), and by Early Researcher Award ER13-09-040 from the Ministry of Research and Innovation and Science of the Government of Ontario (www.ontario.ca/page/early-researcher-awards), both awarded to CAAB, and by the Interdisciplinary Theoretical and Mathematical Sciences (iTHES, ithes.riken.jp; iTHEMS, ithems.riken.jp) research programmes at RIKEN (CAAB). Additional support in the form of an Ontario Graduate Scholarship from the Government of Ontario (www.osap.gov.on.ca) (LEL), a Michael Smith Foreign Study Supplement and a Doctoral Canadian Graduate Scholarship (CGS-D) from the Natural Sciences and Engineering Research Council of Canada (www.nserc-crsng.gc.ca) were awarded to LEL. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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